Problem: Determine the intercepts of the line. $7x-5=4y-6$ $x$ -intercept: $\Big($
Explanation: The $x$ -intercept of a graph is the point of intersection between the $x$ -axis and the graph. Since the $x$ -axis is also the line $y=0$, the $y$ -value of this point will always be $0$. The $y$ -intercept of a graph is the point of intersection between the $y$ -axis and the graph. Since the $y$ -axis is also the line $x=0$, the $x$ -value of this point will always be $0$. To find the $x$ -intercept, let's substitute $ y= 0$ into the equation and solve for $x$ : $ \begin{aligned}7x-5&=4\cdot{0}-6\\ 7x-5&=-6\\ 7x&=-1\\ x&=-\dfrac{1}{7}\end{aligned}$ So the $x$ -intercept is $\left(-\dfrac{1}{7},0\right)$. To find the $y$ -intercept, let's substitute $ x= 0$ into the equation and solve for $y$ : $ \begin{aligned}7\cdot0-5&=4y-6\\ -5&=4y-6\\ 1&=4y\\ \dfrac{1}{4}&=y\end{aligned}$ So the $y$ -intercept is $\left(0,\dfrac{1}{4}\right)$. In conclusion, The $x$ -intercept of the graph is $\left(-\dfrac{1}{7},0\right)$. The $y$ -intercept of the graph is $\left(0,\dfrac{1}{4}\right)$.